The Madrid coach does not think his side deserved to win their Champions League match on Tuesday, and claimed the Red Devils were superior to los Blancos during the game
United attacker Nani was sent off in the second half for a high challenge on Alvaro Arbeloa, which proved to be a huge turning point in the game as Madrid went on to score twice after that contentious decision.
And Mourinho insisted that regardless of that game-changing moment, his side were lucky to escape with a victory.
"Independent of the red card decision, the best team lost," Mourinho told ITV after the final whistle.
The Red Devils had taken the lead shortly after half-time when Sergio Ramos deflected Nani's cross past his own goalkeeper, before the same United player was shown a straight red card by referee Cuneyt Cakir.
Los Blancos overturned United's lead following Nani's dismissal as Luka Modric and Cristiano Ronaldo scored in quick succession, but their coach said after the game they were fortunate to triumph.
"We didn't play well, but football is like this."
Mourinho told Sky Sports that after his team's recent performances against Barcelona - where they won both clashes in the Copa del Rey and La Liga - he was disappointed that they failed to put in a similar showing against United.
"I was waiting for my team to come here and to express our football in a different way.
"I know they [United] are giants, not just physically, but mentally.
"11 vs 11, I doubt that we could win the match.
"I know they are fantastic, I know they have a manager who can motivate people, but I was waiting for us to come here and play a different way."
When asked about the next round and who he thought might win the competition, he said: "We've removed a big one [obstacle in the way of their CL progress], but the Champions League is full of good teams.
"Nobody speaks about Dortmund, I played them in the group phase, they are fantastic.
"Nobody talks about Celtic, from Milan-Barca a big team will come too, I don't know, Paris, Valencia, Bayern. There are so many teams, so many obstacles, but this one was important, particularly after the first leg."
The former Chelsea manager also spoke of his pleasure at being back in England, if only for a short time.
"I love it, everybody knows I love it, and everybody knows that someday I will be back, unless nobody wants me!" he joked.
"Independent of the result, it's brilliant to play here."
The draw for the quarter-finals will take place in Nyon on Friday, March 15.